Final answer:
The expected value of buying one $10 lottery ticket with 700 sold in total, where prizes are $500, $250, and $100, is an expected loss of $8.785 per ticket.
Step-by-step explanation:
To calculate the expected value when buying a ticket in the school fundraiser, we consider the probability of winning each prize and its corresponding value. With 700 tickets sold, there is a 1/700 chance to win the first prize of $500, a 1/699 chance to win the second prize of $250 (since one ticket has been removed), and a 1/698 chance to win the third prize of $100 (after removing two tickets). The expected value is computed as follows:
- Expected value for 1st prize: (1/700) × $500 = $0.714
- Expected value for 2nd prize: (1/699) × $250 = $0.358
- Expected value for 3rd prize: (1/698) × $100 = $0.143
The combined expected value from prizes is $0.714 + $0.358 + $0.143 = $1.215.
Since each ticket costs $10, the net expected value is the expected winnings minus the cost of the ticket:
Net expected value = Expected winnings - Cost of ticket = $1.215 - $10 = -$8.785.
Therefore, you would expect to lose $8.785 on average for each ticket purchased. This is your expected loss per ticket.